已知sin(xy)=ln((x+1)/y)+1,求y'(0).
问题描述：
已知sin(xy)=ln((x+1)/y)+1,求y'(0).
答
sin(xy)-ln((x+1)/y)+1=0对x求导有：（y+xy')cos(xy)-y/(x+1)·[y-(x+1)y']/y^2-y/(x+1)·(x+1)(-1/y^2)y'=0x=0代入有：y-[y-y']/y+y'/y=02y'=y-y^2又sin(xy)=ln((x+1)/y)+1x=0代入有:y(0)=e≈2.718y'(0)=(e-e^2 )/2...